What is greatest common divisor?

Greatest Common Divisor

In mathematics, the greatest common divisor (gcd), also known as the greatest common factor (gcf), or highest common factor (hcf), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder. For example, the GCD of 8 and 12 is 4.

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Some articles on greatest common divisor:

Common-mode Signal
... Common-mode signal is the component of an analog signal which is present with one sign on all considered conductors ... In telecommunication, common-mode signal on a transmission line is known as longitudinal voltage ... where the signal is transferred with differential voltage use, the common-mode signal is called a half-sum of voltages When referenced to the local common or ground, a common ...
Greatest Common Divisor - The Gcd in Commutative Rings
... The notion of greatest common divisor can more generally be defined for elements of an arbitrary commutative ring, although in general there need not exist one for ... in R, then an element d of R is called a common divisor of a and b if it divides both a and b (that is, if there are elements x and y in R such that d·x = a and d·y = b) ... If d is a common divisor of a and b, and every common divisor of a and b divides d, then d is called a greatest common divisor of a and b ...
Recursive Call - Recursive Programs - Recursive Procedures - Greatest Common Divisor
... The Euclidean algorithm, which computes the greatest common divisor of two integers, can be written recursively ... otherwise, return end gcd Recurrence relation for greatest common divisor, where expresses the remainder of Computing the recurrence relation for x = 27 ...
Greatest Common Divisor Of Two Polynomials - General Definition
... A greatest common divisor of p and q is a polynomial d that divides p and q and such that every common divisor of p and q also divides d ... If F is a field and p and q are not both zero, d is a greatest common divisor if and only if it divides both p and q and it has the greatest degree among the ... The greatest common divisor of p and q is usually denoted "gcd(p, q)" ...
Greatest Common Divisor Of Two Polynomials
... In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that evenly divides each of the two original polynomials ... This concept is analogous to the greatest common divisor of two integers ... Therefore, "greatest" is meant for the relation of divisibility ...

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